Dump Algebra

Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is Andrew Hacker, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It, co-authored with Claudia Dreifusconvinced me that tenure is harmful. His latest broadside, “Is Algebra Necessary?”, in last Sunday’s New York Times, is as provocative.

He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right.

Support for Hacker’s view comes from the observations of engineer and senior executive Robert Pearson (published in his article “Why don’t most engineers use undergraduate mathematics in their professional work?”, UME Trends, October 1991). Based on his “fifty-four years of experience as a design engineer, as an engineering manager, as a member of management assigned to help alleviate engineer-shop design and manufacturing problems, as a product cost and reliability analyst, as a corporate executive, and as an undergraduate mathematics instructor,” he asks, “Why do 50 percent (probably closer to 70%) of engineering and science practitioners seldom, if ever, use mathematics above the elementary algebra/trigonometry level in their practice?” If algebra is the limit for most engineering and science professionals, why does a typical citizen need algebra?

As Hacker says, much more useful than algebra is quantitative literacy: being able to estimate, judge the reasonableness of numbers, and thereby detect bullshit. Our world offers plenty of practice.

My only disagreement with Hacker is small: whether, as he says, young people should learn to “do long division, whether they want to or not.” I teach mathematics and have written a mathematics textbook, but long division I haven’t used for at least three decades.


Thomas Boyle

I'm an engineer, and he's right. The distinction that's being lost in the comments is the difference between teaching basic algebra (and trigonometry), and what makes its way into high school textbooks. Over the years, many people have told me they hated trigonometry and just didn't "get" it. I've told them, in response, that I can teach them all the trigonometry I have ever used in engineering, in 10 minutes. I've never failed yet: Sin, Cos, Tan, ArcSin, ArcCos, ArcTan, and Sin^2 + Cos^2 = 1 don't take long to explain. The trigonometric proofs I struggled through in school have never been useful for anything. Looking quickly at a high school algebra book, I have a similar feeling. Basic algebra is important (and much more involved than basic trig) - but the tortured proofs of the high school textbook are overkill for anyone not looking at a math career.

Nosybear

We live in an age where the average journalism student can be completely bamboozled by a bar graph or a percentage. Nah, mathematical literacy as exemplified by algebra and basic statistic, not necessary. Knowing that kind of stuff really inhibits the effectiveness of the daily bombardment of marketing messages using math to lend an air of pseudo-authority to bullshit. Algebra and statistics teach us to ask for denominators and confidence intervals, rendering political ads ineffective as we realize that, compared to thirteen trillion, seven hundred billion really isn't such a big, scary number. Or that doubling the odds of incidence of a disease that is rare to start with probably isn't a reason to take a drug off the market. Nah, we don't need mathematical reasoning, it just interferes with the ability of people to lie with numbers.

Walter Wimberly

Math for math sake is rarely important unless you get to the higher levels of a given field, however that doesn't mean that math still isn't important. For most students, once you reach algebra, you will not use that math.

However, one thing I've noticed in my teaching programming and related courses, is that those with a better understanding of math tend to know how to look at complex problems, and break them down into smaller solvable problems. This is very important not just for any of the STEM majors, but for other majors as well.

While I've heard many students lament the taking of math, it does serve a useful purpose. It is (part of) the job of the math teacher to instill within the student the long term purpose for the training - not just the formulaic methods.

Uwjames

Math tacher/math major/programmer here. I've often wondered if we'd be as well or better off replacing algebra with introductory programming. All the same neurological benefits are bound to be achieved in either case (symbolic and abstract reasoning, breaking down complex problems into simpler problems, backwards engineering, etc) but programming is a more relevant and useful skill. We could also effectively teach a lot of the most important algebra and geometry standards through a properly designed programming curriculum.

Well, it's an experiment that I think would be worth trying.

Bill Strickland

I agree: introductory programming would probably provide the same benefits as those to which I earlier alluded and could even provide significant additional thinking skills. However, it requires a greater infrastructure than pencil and paper, and there's something attractive in the ability to push symbols around practically anytime, anywhere.

The gist of my argument against dumping algebra is that humans can learn lots more than just what they set out to learn; that dumping algebra is, I believe, dumping more than just algebra, if you get my meaning.

KS Granny

One relevant question, I think: I went straight from grade-school arithmetic to algebra, the year after Sputnik went up, so I never had pre-algebra. What does pre-algebra cover? Does it expose students to the concept of using a letter to represent an unknown quantity? Does it introduce the concept of equations more complex than "3+2=5"? If so, then perhaps that's all the non-mathematical need.

Now myself, I use basic algebra in my homemaking tasks - comparing prices in a store, adjusting quantities in a recipe, and so forth. I used long division just yesterday, and it certainly was not the first time since I finished school. So I am personally in favor of teaching both those subjects.

I do think that our "one size fits all" educational system is fundamentally flawed. As Clancy points out, it would be nice if everyone knew algebra (and spelling and history, I might add), but the fact is some students will devour it (as I did), and others will not be able to digest it. Making it a requirement for graduation is of dubious value. Making it relevant would be much more effective in graduating algebra-capable people, if that is what we are determined to do.

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Anita

My daughter is a grad student in statistics. She loves math (obviously) and detests arithmetic. Without algebra in high school, she probably would not have become a mathematician. We expose young people who will not become artists to art, who will not become musicians to music, and so on and on, because the exposure gives them the opportunity to explore possible future interests. Algebra is a first taste of mathematics, as contrasted to arithmetic, and is a first step towards a career in STEM. Take it away from our youth, and you narrow their future choices, just as you narrow their futures if you take away art and music and history and literature.

Travis

Quantitative literacy is clearly more important, but how are you going to be good at quantitative analysis without a strong understanding of algebra? All students should learn some level of statistics, at the very least. Too much of our world is driven by policy decisions that are based on scientific, sociological, and economic applications of statistics principles. It's clear that our society in particular needs better math literacy to improve their ability to analyze the statistics thrown in their face every day. And I can't imagine trying to learn statistics without an understanding of algebra...